Communication: Propagator for diffusive dynamics of an interacting molecular pair

Area of Science:

• Computational physics
• Chemical kinetics
• Integral equations

Background:

• Fredholm integral equations of the second kind are crucial in modeling physical phenomena.
• Direct iterative methods can fail, yielding divergent perturbation series solutions.
• Accurate description of particle dynamics and reaction rates is essential in physical chemistry.

Purpose of the Study:

• Introduce a new, robust solution method for Fredholm integral equations.
• Develop an accurate propagator expression for diffusive dynamics of interacting particles.
• Validate the propagator's accuracy by calculating reaction rates.

Main Methods:

• Developed a novel analytical solution technique for Fredholm integral equations.
• Derived an accurate propagator expression for pairwise particle diffusion.
• Incorporated arbitrary central potentials and hydrodynamic interactions.
• Calculated diffusion-controlled geminate and bimolecular reaction rates.

Main Results:

• The new method provides a convergent solution where iterative approaches diverge.
• The derived propagator expression accurately describes particle dynamics over the entire time range.
• Calculated reaction rates show excellent agreement with theoretical predictions.

Conclusions:

• The proposed solution method is effective for Fredholm integral equations, especially when iterative methods fail.
• The accurate propagator expression is valuable for studying diffusive dynamics and reaction kinetics.
• This approach enhances the predictive power for chemical reaction rates in various systems.